Respuesta :
Answer:
the radius is 1.08 meters
Step-by-step explanation:
Hello
the volume of a cube is given by
[tex]v_{c}=side*side*side\\\\ v=side^{3}[/tex]
The volume of a sphere is given by:
[tex]v_{s}=\frac{4}{3} \pi\ r^{3}\\[/tex]
Step 1
according to the problem
[tex]v_{c}=v_{s}\\Hence\\side^{3} =\frac{4}{3} \pi\ r^{3}\\[/tex]
we need to know the radius, o we isolate r
[tex]side^{3} =\frac{4}{3} \pi\ r^{3} \\3*side^{3} = 4 \pi \ r^{3}\\\\\ \frac{3*side^{3}}{4 \pi } = r^{3} \\\\r^{3} = \frac{3*side^{3}}{4 \pi } \\\\\ \sqrt[3]{r^{3}} =\sqrt[3]{\frac{3*side^{3}}{4 \pi\ }} \\r=\sqrt[3]{\frac{3*side^{3}}{4\pi}}[/tex]
Step 2
put the value of side = 1.75 into the equation
[tex]r=\sqrt[3]{\frac{3*side^{3}}{4\pi}}\\r=\sqrt[3]{\frac{3*(1.75m)^{3}}{4\pi}}\\r=\sqrt[3]{\frac{16.07}{4\pi}}\\r=\sqrt[3]{1.27}\\ r=1.08\ m[/tex]
the radius is 1.08 meters
Have a nice day
